Recording Subtraction Calculations A guide to the progression and written methods for subtraction used at: Verwood CE VA First School Trinity First School Hillside First School Emmanuel CE VA Middle School We have been working together with the others schools in verwood to produce a progression of methods used, the aim of this is to ensure consistency across the pyramid/cluster?

Subtraction vocabulary Here’s some key vocabulary that can be used when talking about subtraction with your child count back takeaway difference subtract less than minus Subtraction vocabulary + Some vocab children will need to help them. We find that children often make mistakes when encountering questions with the word number sentence/calculation

Some examples of teaching subtraction in the EY at school – in foundation stage there would be a lot of number formation practise, counting on and back in 1’s, ordering and finding missing numbers and many practical activities. These examples from year 1 show children using practical activities to help them understand the concept of taking away including physically breaking off cubes, using laminated number tracks with pens and subtraction bingo as a mental maths starter.

Making the link… It is really important that we all help children to make the link between addition and subtraction. You can help them with this understanding in many different ways Eg, If I have 7 objects and add 3 more I make 10. What number do you think I would have left if I took the 3 away?

Progression of written methods

As well as using the more formal method of using a numberline we still encourage children to use methods they are comfortable with – this includes using dienes equipments, multilink, objects and can record their findings using pictures. This example is taken from our learning board in year 1 where we were using Percy Park Keeper pictures to solve takeaway number sentences. Before we start using a number line we use physical objects to show what takeaway is and to start developing their concept of subtraction.

We can see from this that the answer = 5. Once your child has grasped basic counting back of objects and ordering of numbers, using practical equipment, they will move onto taking away using a basic number line as a more formal way of recording The basic number line is one where all the numbers are marked on the line e.g calculate 8 - 3 = ? 0 1 2 3 4 5 6 7 8 9 10 11 12 We can see from this that the answer = 5. Using this method your child has to mark all the numbers on the number line. -1 -1 -1 This is a more formal method, it is by no means the be-all and end-all – we encourage children to use informal jottings to support their calculations as well as practical equipment. SC-we would always encourage the children to start with the first number and count back along the number line – the opposite way to addition. Children will be ready to start with this more formal method at different stages –there is no set year or time when this should be introduced.

Once your child has grasped this concept the next step is to use a blank number line 15-7= -1 -1 -1 -1 -1 -1 -1 8 9 10 11 12 13 14 15 So we start at the biggest number…15 (at the other end of the number line) And count down 7 places The number we end on is our answer!

Once your child has is confident subtracting on a blank number line using jumps of 1, they may progress to counting back in bigger jumps by partitioning the smaller number 23-12= -10 -1 -1 11 12 13 23 So we start at the biggest number…23 And make one jump back of 10 I’m sure you can see the similarities with the progression of skills for subtraction with addition. Then takeaway the smaller jumps

67-23= 44 44 45 46 47 57 67 So we start at the biggest number…67 -10 -1 -1 -1 -10 44 45 46 47 57 67 So we start at the biggest number…67 And make two jumps of 10 Then subtract our smaller jumps

Have a go…. Have a look at the four number lines which shows common errors a child could make. Use pink and green to mark them. Spot the one that’s right and underline it in pink. On the three that are wrong can you spot the place where the person has gone wrong and underline that part in green? Why do you think they have made these errors? Is it a misconception with place value? Counting back? Partitioning? Understanding?

Counting on as a strategy… 65 – 49 = 16 +10 +1 +1 +1 +1 +1 +1 49 59 60 61 62 63 64 65 So we start at the smallest number….49 And count up to the biggest number 65 Then add our jumps together to get the answer

Sometimes you may need to subtract a near multiple of 10 (such as 9 or 19) The quickest way to do this is by subtracting a multiple of 10 and readjusting. 28 - 9 = 19 -10 +1 18 19 28 This is also a mental strategy that can be practised at home and at school. Children need explaining that we have taken away ten which is 1 too many and therefore we do need to readjust by adding one back on. So we start at the biggest number…28 And make one jump back of 10 Then readjust by adding 1

The next step in using a number line to add is to partition the numbers according to their place value 99 – 43 = 56 -40 -3 56 59 99 So we start at the biggest number…99 And make one jump back of 40 Then make one jump of 3

The next step is partitioning when subtracting numbers Partitioning involves breaking numbers down according to the ‘value’ of each individual digit. e.g calculate 25 - 12 10 2 So, 25 – 12 = 13 25 – 10 = 15 15 – 2 = 13

Eventually the children will progress to Column Subtraction and the first step in doing this is to partition in vertical columns. e.g calculate 77 - 46 77 – 46 = 70 + 7 - 40 + 6 + 30 1 = 31 This is linking in with the steps previous, but moving them towards the standard written methods we would have learned at school. When the children start to record vertically, we would encourage them to start by adding the units

e.g calculate 68 - 34 T U 6 8 - 3 4 4 3 Answer = 34 Column Subtraction is where the numbers are placed vertically according to their place value. You ALWAYS start subtracting the numbers in the far right hand column FIRST (units in this case) and then work across to the left. e.g calculate 68 - 34 T U 6 8 - 3 4 4 Take away the 8 from the 4 first which gives you an answer of 4 Then subtract the 3 from the 6 (remembering these are tens!) 3 Answer = 34

We would always start this where the top units number is bigger than the bottom units number, so that the children become familiar with the process. We would model this using cubes 68-34=

Sometimes when doing column subtraction, if the tops units number is smaller than the bottom units number, you have to exchange a 10. At Verwood First we call this visiting the swap shop! This should look more familiar! I know this seems like a quick method, but it is vital that all the building blocks are put in place before we get to this point. An understanding of place value is essential. All the time that we are doing this we are emphasising place value! We tend not to say, carry a one, we would say carry the ten/hundred etc. We would also say add 6 tens and 5 tens and 1 ten, rather than 6, 5, 1.

Remember if the top units is a smaller number than the bottom units you need to visit the swap shop

At the Swap Shop you can swap one ten for ten units

How can we record this? 63-38= T U 5 1 6 3 - 3 8

Try this one: T U 42-28= 3 1 4 2 - 2 8 1 4